The human brain contains >10^10 neurons connected by > 10^13 synapses into an awesome network that underlies neural computation and cognitive function. It is widely believed that synapses form the substrate of important aspects of cognition and its dysfunctions. For example, experience-dependent plasticity, such as memory, may express itself in the properties of individual synapses. To support these cognitive functions individual synapses are thought to function autonomously and have heterogeneous properties. Unraveling basic aspects of synaptic function therefore demands the study of individual synapses. However, synapses are the smallest functional units of the brain (size ~ 1 micrometer), containing only a handful of signal transduction molecules of a given type, and functional assays for single synapses have remained challenging. As a consequence, fundamental aspects of synaptic function and plasticity have remained controversial. The goal of this proposal is to explore fundamental aspects of synaptic function and plasticity using recently developed optical techniques based on 2-photon [Ca2+] imaging in spines. These techniques have the sensitivity to detect the opening of single Ca2+ permeable channels and receptors at hippocampal cortical synapses in rodent brain slices. The fact that [Ca2+] accumulations mediated by synaptically activated NMDA-Rs can be measured allows the determination of the number of NMDA-Rs opened during synaptic transmission and the number of receptors at synapses. This issue has important consequences for the sources of noise in synaptic transmission and the dynamic range of synaptic transmission. NMDA-R activation can also be used to detect the spread of glutamate in the extracellular space. Hence it is possible to determine if individual synapses are independent or if glutamate released at one synapse spills over to activate receptors at neighboring synapses. This issue has important consequences for the memory capacity of neural networks and the mechanisms of synaptic plasticity. Finally, imaging of NMDA-R activation can be used to develop a method of optical quantal analysis at single synapses, allowing a direct test of the uni--vesicular hypothesis and a dissection of the mechanisms of short-term synaptic plasticity. We hope to end up with a core description of the function and plasticity of single synapses.